Reliable navigation systems and devices have always been essential for estimating both distance traveled and position. For example, early navigating was accomplished with “deduced” or “dead” reckoning. In dead-reckoning, a navigator finds a current position by measuring the course and distance the navigator has moved from some known point. Starting from the known point, the navigator measures out a course and distance from that point. Each ending position will be the starting point for the course-and-distance measurement. In order for this method to work, the navigator needs a way to measure a course and a way to measure the distance traveled. The course is measured by a magnetic compass. In pedestrian dead reckoning, the distance is the size of a single step. A position estimate is derived by the integration of distance and direction over a sequence of steps. This type of navigation, however, is highly prone to errors, which when compounded can lead to highly inaccurate position and distance estimates.
In more advanced navigation systems, such as an inertial navigation system (INS), positional errors can accumulate over time. For example, any navigation performed in areas where satellite or radar tracking measurements are inaccessible or restrictive (such as areas where global positioning system, or GPS, measurements are “denied”) is susceptible to the accumulation of similar positional errors. Moreover, in the dead-reckoning methods discussed above, these positional errors accumulate based on the distance traveled. There is a need in the art for improvements in position estimation for navigation devices.